Luonan Chen

Chaotic simulated annealing by a neural network model with transient chaos

Abstract We propose a neural network model with transient chaos, or a transiently chaotic neural network (TCNN) as an approximation method for combinatorial optimization problems, by introducing transiently chaotic dynamics into neural networks. Unlike conventional neural networks only with point attractors, the proposed neural network has richer and more flexible dynamics, so that it can be expected to have higher ability of searching for globally optimal or near-optimal solutions. A significant property of this model is that the chaotic neurodynamics is temporarily generated for searching and self-organizing, and eventually vanishes with autonomous decrease of a bifurcation parameter corresponding to the “temperature” in the usual annealing process. Therefore, the neural network gradually approaches, through the transient chaos, to a dynamical structure similar to such conventional models as the Hopfield neural network which converges to a stable equilibrium point. Since the optimization process of the transiently chaotic neural network is similar to simulated annealing, not in a stochastic way but in a deterministically chaotic way, the new method is regarded as chaotic simulated annealing (CSA). Fundamental characteristics of the transiently chaotic neurodynamics are numerically investigated with examples of a single neuron model and the Traveling Salesman Problem (TSP). Moreover, a maintenance scheduling problem for generators in a practical power system is also analysed to verify practical efficiency of this new method.

Stability of genetic regulatory networks with time delay

Presents a model for genetic regulatory networks with time delays, which is described by functional differential equations or delay differential equations (DDE), provide necessary and sufficient conditions for simplifying the genetic network model, and further analyze nonlinear properties of the model in terms of local stability and bifurcation. The proposed model transforms the original interacting network into several simple transcendental equations at an equilibrium, thereby significantly reducing the computational complexity and making analysis of stability and bifurcation tractable for even large-scale networks. Finally, to test the theory, a repressilator model is used as an example for numerical simulation.

Inferring gene regulatory networks from multiple microarray datasets

MOTIVATION Microarray gene expression data has increasingly become the common data source that can provide insights into biological processes at a system-wide level. One of the major problems with microarrays is that a dataset consists of relatively few time points with respect to a large number of genes, which makes the problem of inferring gene regulatory network an ill-posed one. On the other hand, gene expression data generated by different groups worldwide are increasingly accumulated on many species and can be accessed from public databases or individual websites, although each experiment has only a limited number of time-points. RESULTS This paper proposes a novel method to combine multiple time-course microarray datasets from different conditions for inferring gene regulatory networks. The proposed method is called GNR (Gene Network Reconstruction tool) which is based on linear programming and a decomposition procedure. The method theoretically ensures the derivation of the most consistent network structure with respect to all of the datasets, thereby not only significantly alleviating the problem of data scarcity but also remarkably improving the prediction reliability. We tested GNR using both simulated data and experimental data in yeast and Arabidopsis. The result demonstrates the effectiveness of GNR in terms of predicting new gene regulatory relationship in yeast and Arabidopsis. AVAILABILITY The software is available from http://zhangorup.aporc.org/bioinfo/grninfer/, http://digbio.missouri.edu/grninfer/ and http://intelligent.eic.osaka-sandai.ac.jp or upon request from the authors.

Short-term load forecasting based on an adaptive hybrid method

This paper aims to develop a load forecasting method for short-term load forecasting, based on an adaptive two-stage hybrid network with self-organized map (SOM) and support vector machine (SVM). In the first stage, a SOM network is applied to cluster the input data set into several subsets in an unsupervised manner. Then, groups of 24 SVMs for the next days load profile are used to fit the training data of each subset in the second stage in a supervised way. The proposed structure is robust with different data types and can deal well with the nonstationarity of load series. In particular, our method has the ability to adapt to different models automatically for the regular days and anomalous days at the same time. With the trained network, we can straightforwardly predict the next-day hourly electricity load. To confirm the effectiveness, the proposed model has been trained and tested on the data of the historical energy load from New York Independent System Operator.

Detecting early-warning signals for sudden deterioration of complex diseases by dynamical network biomarkers

Considerable evidence suggests that during the progression of complex diseases, the deteriorations are not necessarily smooth but are abrupt, and may cause a critical transition from one state to another at a tipping point. Here, we develop a model-free method to detect early-warning signals of such critical transitions, even with only a small number of samples. Specifically, we theoretically derive an index based on a dynamical network biomarker (DNB) that serves as a general early-warning signal indicating an imminent bifurcation or sudden deterioration before the critical transition occurs. Based on theoretical analyses, we show that predicting a sudden transition from small samples is achievable provided that there are a large number of measurements for each sample, e.g., high-throughput data. We employ microarray data of three diseases to demonstrate the effectiveness of our method. The relevance of DNBs with the diseases was also validated by related experimental data and functional analysis.

Forecasting the Wind Generation Using a Two-Stage Network Based on Meteorological Information

This paper proposes a practical and effective model for the generation forecasting of a wind farm with an emphasis on its scheduling and trading in a wholesale electricity market. A novel forecasting model is developed based on indepth investigations of meteorological information. This model adopts a two-stage hybrid network with Bayesian clustering by dynamics and support vector regression. The proposed structure is robust with different input data types and can deal with the nonstationarity of wind speed and generation series well. Once the network is trained, we can straightforward predict the 48-h ahead wind power generation. To demonstrate the effectiveness, the model is applied and tested on a 74-MW wind farm located in the southwest Oklahoma of the United States.

Optimal operation solutions of power systems with transient stability constraints

The computation of an optimal operation point in power systems is a nonlinear optimization problem in functional space, which is not easy to deal with precisely, even for small-scale power systems. On the other hand, the emergence of competitive power markets makes optimal power flow (OPF) with transient stability constraints increasingly important because the conventionally heuristic evaluation for the operation point can produce a discrimination among market players in the deregulated power systems. Instead of directly tackling this tricky problem, in this paper, OPF with transient stability constraints (OTS) is equivalently converted into an optimization problem in the Euclidean space via a constraint transcription, which can be viewed as an initial value problem for all disturbances and solved by any standard nonlinear programming techniques adopted by OPF. The transformed OTS problem has the same variables as those of OPF in form, and is tractable even for the large-scale power systems with a large number of transient stability constraints. This paper also derives the Jacobian matrices of the transient stability constraints and gives two computation algorithms based on the relaxation scheme. The numerical simulation verified the effectiveness of the proposed approach.

Chaos and asymptotical stability in discrete-time neural networks

Abstract This paper aims to theoretically prove by applying Marottos Theorem that both transiently chaotic neural networks (TCNN) and discrete-time recurrent neural networks (DRNN) have chaotic structure. A significant property TCNN and DRNN is that they have only one bounded fixed point, when absolute values of the self-feedback connection weights in TCNN and the difference time in DRNN are sufficiently large. We show that this unique fixed point can actually evolve into a snap-back repeller which generates chaotic structure, if several conditions are satisfied. On the other hand, by using the Lyapunov functions, we also derive sufficient conditions on asymptotical stability for symmetrical versions of both TCNN and DRNN, under which TCNN and DRNN asymptotically converge to a fixed point. Furthermore, related bifurcations are also considered in this paper. Since both TCNN and DRNN are not special but simple and general, the obtained theoretical results hold for a wide class of discrete-time neural networks. To demonstrate the theoretical results of this paper better, several numerical simulations are provided as illustrating examples.

Inferring gene regulatory networks from gene expression data by path consistency algorithm based on conditional mutual information

MOTIVATION Reconstruction of gene regulatory networks (GRNs), which explicitly represent the causality of developmental or regulatory process, is of utmost interest and has become a challenging computational problem for understanding the complex regulatory mechanisms in cellular systems. However, all existing methods of inferring GRNs from gene expression profiles have their strengths and weaknesses. In particular, many properties of GRNs, such as topology sparseness and non-linear dependence, are generally in regulation mechanism but seldom are taken into account simultaneously in one computational method. RESULTS In this work, we present a novel method for inferring GRNs from gene expression data considering the non-linear dependence and topological structure of GRNs by employing path consistency algorithm (PCA) based on conditional mutual information (CMI). In this algorithm, the conditional dependence between a pair of genes is represented by the CMI between them. With the general hypothesis of Gaussian distribution underlying gene expression data, CMI between a pair of genes is computed by a concise formula involving the covariance matrices of the related gene expression profiles. The method is validated on the benchmark GRNs from the DREAM challenge and the widely used SOS DNA repair network in Escherichia coli. The cross-validation results confirmed the effectiveness of our method (PCA-CMI), which outperforms significantly other previous methods. Besides its high accuracy, our method is able to distinguish direct (or causal) interactions from indirect associations. AVAILABILITY All the source data and code are available at: http://csb.shu.edu.cn/subweb/grn.htm. CONTACT lnchen@sibs.ac.cn; zpliu@sibs.ac.cn SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

Global searching ability of chaotic neural networks

This paper aims to theoretically prove that both transiently chaotic neural networks (TCNNs) and discrete-time recurrent neural networks (DRNNs) have a global attracting set which ensures that the neural networks carry out a global search. A significant property of TCNNs and DRNNs is that their attracting sets are generated by a bounded fixed point, which is the unique repeller when absolute values of the self-feedback connection weights in TCNN and the difference time in DRNN are sufficiently large. We provide sufficient conditions under which the neural networks have a trapping region where the global unstable set of the fixed point actually evolves into a global attracting set. We also prove the coexistence of an attracting set and a transversal homoclinic orbit in the same region, which may result in complicated chaotic dynamics. For combinatorial optimization with neural networks, this paper shows that TCNNs and DRNNs do have global searching ability and their attracting set encloses not only local minima, but also global minima for the commonly used objective functions. To demonstrate the theoretical results of this paper, several numerical simulations are provided as illustrative examples.